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Asymptotic Inference for Nonstationary Fractionally Integrated Processes

Author

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  • Francesc Marmol

    () (Universidad Carlos III)

  • Juan J. Dolado

    () (Universidad Carlos III)

Abstract

This paper studies the asymptotics of nonstationary fractionally integrated (NFI) multivariate processes with memory parameter d > 0.5 . We provide conditions to establish a functional central limit theorem and weak convergence of stochastic integrals for NFI processes under the assumption that the innovations are linear processes. Several applications of these results are given. More specifically, we prove the rates of convergence of the OLS estimators of cointegrating vectors in triangular representations. When the regressors are strongly exogenous with respect to the corresponding parameters of the cointegrating vector, then the limiting OLS distribution is a mixture of normals from which standard inference can be implemented. On the other hand, we also extend Sims, Stock and Watson's (1990) study on estimation and hypothesis testing in vector autoregressions with integrated processes and deterministic components to the more general fractional framework. We show how their main conclusions remain valid when dealing with NFI processes, namely, that whenever a block of coefficients can be written as coefficients on zero mean I(0) regressors in a model that includes a constant term, they will have a joint asymptotic normal distribution, so that the corresponding restrictions can be tested using standard asymptotic chi-squared distribution theory. Otherwise, in general, the associated statistics will have nonstandard limiting distributions.

Suggested Citation

  • Francesc Marmol & Juan J. Dolado, 1999. "Asymptotic Inference for Nonstationary Fractionally Integrated Processes," Computing in Economics and Finance 1999 513, Society for Computational Economics.
  • Handle: RePEc:sce:scecf9:513
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    References listed on IDEAS

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    1. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-1393, November.
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    7. Phillips, P.C.B., 1988. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations," Econometric Theory, Cambridge University Press, vol. 4(03), pages 528-533, December.
    8. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(04), pages 583-621, August.
    9. Marinucci, D & Robinson, Peter M., 1998. "Semiparametric frequency domain analysis of fractional cointegration," LSE Research Online Documents on Economics 2258, London School of Economics and Political Science, LSE Library.
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    11. D Marinucci, 1998. "Band Spectrum Regression for Cointegrated Time Series with Long Memory Innovations," STICERD - Econometrics Paper Series 353, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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    Cited by:

    1. Krämer, Walter & Marmol, Francesc, 1998. "OLS-based asymptotic inference in linear regression models with trending regressors and AR(p)-disturbances," Technical Reports 1998,43, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Marmol, Francesc & Hassler, Uwe, 1998. "Fractional cointegrating regressions in the presence of linear time trends," DES - Working Papers. Statistics and Econometrics. WS 9794, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Bent Jesper Christensen & Robinson Kruse & Philipp Sibbertsen, 2013. "A unified framework for testing in the linear regression model under unknown order of fractional integration," CREATES Research Papers 2013-35, Department of Economics and Business Economics, Aarhus University.

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